Ammonia is a base, and sulfuric acid is well, an acid. When an acid and base react, they form a salt. In the case of ammonia and sulfuric acid, they will react to form ammonium sulphate.
It is a solid and will dissolve in water. One would then need to separate it from the sulfuric acid that remains and then treat it with sodium hydroxide to get ammonia again.But you will likely use aqueous sodium hydroxide, which means that you have to find a way to dry the product as a result. Back to square one.
Hope this helps